1 machine learning what is learning?. 2 machine learning what is learning? “that is what learning...
TRANSCRIPT
1
Machine Learning
• What is learning?
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Machine Learning
• What is learning?
• “That is what learning is. You suddenly understand something you've understood all your life, but in a new way.”(Doris Lessing – 2007 Nobel Prize in Literature)
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Machine Learning
• How to construct programs that automatically improve with experience.
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Machine Learning
• How to construct programs that automatically improve with experience.
• Learning problem:
– Task T
– Performance measure P
– Training experience E
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Machine Learning
• Chess game:
– Task T: playing chess games
– Performance measure P: percent of games won
against opponents
– Training experience E: playing practice games
againts itself
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Machine Learning
• Handwriting recognition:
– Task T: recognizing and classifying handwritten
words
– Performance measure P: percent of words correctly classified
– Training experience E: handwritten words with given classifications
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Designing a Learning System
• Choosing the training experience:
– Direct or indirect feedback
– Degree of learner's control
– Representative distribution of examples
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Designing a Learning System
• Choosing the target function:
– Type of knowledge to be learned
– Function approximation
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Designing a Learning System
• Choosing a representation for the target
function:
– Expressive representation for a close function
approximation
– Simple representation for simple training data and
learning algorithms
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Designing a Learning System
• Choosing a function approximation algorithm (learning algorithm)
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Designing a Learning System
• Chess game:
– Task T: playing chess games
– Performance measure P: percent of games won
against opponents
– Training experience E: playing practice games
againts itself
– Target function: V: Board R
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Designing a Learning System
• Chess game:
– Target function representation:
V^(b) = w0 + w1x1 + w2x2 + w3x3 + w4x4 + w5x5 + w6x6
x1: the number of black pieces on the board
x2: the number of red pieces on the board
x3: the number of black kings on the board
x4: the number of red kings on the board
x5: the number of black pieces threatened by red
x6: the number of red pieces threatened by black
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Designing a Learning System
• Chess game:
– Function approximation algorithm:
(<x1 = 3, x2 = 0, x3 = 1, x4 = 0, x5 = 0, x6 = 0>, 100)
x1: the number of black pieces on the board
x2: the number of red pieces on the board
x3: the number of black kings on the board
x4: the number of red kings on the board
x5: the number of black pieces threatened by red
x6: the number of red pieces threatened by black
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Designing a Learning System
ExperimentGenerator
PerformanceSystem
Generalizer
Critic
New problem(initial board)
Solution trace(game history)
Hypothesis(V^)
Training examples{(b1, V1), (b2, V2), ...}
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Issues in Machine Learning
• What learning algorithms to be used?
• How much training data is sufficient?
• When and how prior knowledge can guide the learning process?
• What is the best strategy for choosing a next training experience?
• What is the best way to reduce the learning task to one or more function approximation problems?
• How can the learner automatically alter its representation to improve its learning ability?
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Concept Learning
• Inferring a boolean-valued function from training examples of its input (instances) and output (classifications).
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Concept Learning
Example
Sky AirTemp
Humidity Wind Water Forecast EnjoySport
1 Sunny Warm Normal Strong
Warm Same Yes
2 Sunny Warm High Strong
Warm Same Yes
3 Rainy Cold High Strong
Warm Change No
4 Sunny Warm High Strong
Cool Change Yes
Experience
Prediction5 Sunny Cold Normal Stron
gWarm Same ?
6 Rainy Warm High Strong
Warm Change ?
Low Weak
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Concept Learning
• Learning problem:
– Task T: classifying days on which my friend enjoys water
sport
– Performance measure P: percent of days correctly
classified
– Training experience E: days with given attributes and
classifications
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Concept Learning
• Learning problem:
– Concept: a subset of the set of instances X
c: X {0, 1}
– Target function:
Sky AirTemp Humidity Wind Water Forecast {Yes, No}
– Hypothesis:
Characteristics of all instances of the concept to be learned
= Constraints on instance attributes
h: X {0, 1}
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Concept Learning
• Satisfaction:
h(x) = 1 iff x satisfies all the constraints of h
h(x) = 0 otherwsie
• Consistency:
h(x) = c(x) for every instance x of the training examples
• Correctness:
h(x) = c(x) for every instance x of X
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Concept Learning
• Hypothesis representation:
<Sky, AirTemp, Humidity, Wind, Water, Forecast>
– ?: any value is acceptable
– single required value
: no value is acceptable
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Concept Learning
• General-to-specific ordering of hypotheses:
hj g hk iff xX: hk(x) = 1 hj(x) = 1
Specific
General
h1 = <Sunny, ?, ?, Strong, ? , ?>
h2 = <Sunny, ?, ?, ? , ? , ?>
h3 = <Sunny, ?, ?, ? , Cool, ?>
h1 h3
h2
H
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FIND-S
• Initialize h to the most specific hypothesis in H:
• For each positive training instance x:
For each attribute constraint ai in h:
If the constraint is not satisfied by x
Then replace ai by the next more general constraint satisfied by x
• Output hypothesis h
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FIND-S
Example
Sky AirTemp
Humidity Wind Water Forecast EnjoySport
1 Sunny Warm Normal Strong
Warm Same Yes
2 Sunny Warm High Strong
Warm Same Yes
3 Rainy Cold High Strong
Warm Change No
4 Sunny Warm High Strong
Cool Change Yes
h = < , , , , , >
h = <Sunny, Warm, Normal, Strong, Warm, Same>
h = <Sunny, Warm, ? , Strong, Warm, Same>
h = <Sunny, Warm, ? , Strong, ? , ? >
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FIND-S
• The output hypothesis is the most specific one that satisfies all positive training examples.
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FIND-S
• The result is consistent with the positive training examples.
• The result is consistent with the negative training examples if the correct target concept is contained in H (and the training examples are correct).
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FIND-S
• Questions:
– Has the learner converged to the correct target concept, as there can be several consistent hypotheses?
– Why prefer the most specific hypothesis?
– What if there are several maximally specific consistent hypotheses?
– Are the training examples correct?
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List-then-Eliminate Algorithm
• Version space: a set of all hypotheses that are consistent with the training examples.
• Algorithm:
– Initial version space = set containing every hypothesis in H
– For each training example <x, c(x)>, remove from the version space any hypothesis h for which h(x) c(x)
– Output the hypotheses in the version space
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List-then-Eliminate Algorithm
• Requires an exhaustive enumeration of all hypotheses in H
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Compact Representation of Version Space
• G (the generic boundary): set of the most generic hypotheses of H consistent with the training data D:
G = {gH | consistent(g, D) g’H: g’ g g consistent(g’, D)}
• S (the specific boundary): set of the most specific hypotheses of H consistent with the training data D:
S = {sH | consistent(s, D) s’H: s g s’ consistent(s’, D)}
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Compact Representation of Version Space
• Version space = <G, S> = {hH | gG sS: g g h g s}
S
G
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Candidate-Elimination Algorithm
• Initialize G to the set of maximally general hypotheses in H
• Initialize S to the set of maximally specific hypotheses in H
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Candidate-Elimination Algorithm
• For each positive example d:
– Remove from G any hypothesis inconsistent with d
– For each s in S that is inconsistent with d:
Remove s from S
Add to S all least generalizations h of s, such that h is consistent with d and some hypothesis in G is more general than h
Remove from S any hypothesis that is more general than another hypothesis in S
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Candidate-Elimination Algorithm
• For each negative example d:
– Remove from S any hypothesis inconsistent with d
– For each g in G that is inconsistent with d:
Remove g from G
Add to G all least specializations h of g, such that h is consistent with d and some hypothesis in S is more specific than h
Remove from G any hypothesis that is more specific than another hypothesis in G
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Candidate-Elimination AlgorithmS0 = {<, , , , , >}G0 = {<?, ?, ?, ?, ?, ?>}
E1 Sunny Warm Normal StrongWarm Same YesS1 = {<Sunny, Warm, Normal, Strong, Warm, Same>}G1 = {<?, ?, ?, ?, ?, ?>}
E2 Sunny Warm High Strong Warm Same YesS2 = {<Sunny, Warm, ?, Strong, Warm, Same>}G2 = {<?, ?, ?, ?, ?, ?>}
E3 Rainy Cold High Strong Warm Change NoS3 = {<Sunny, Warm, ?, Strong, Warm, Same>}G3 = {<Sunny, ?, ?, ?, ?, ?>, <?, Warm, ?, ?, ?, ?>, <?, ?, ?, ?, ?,
Same>}E4 Sunny Warm High Strong Cool Change YesS4 = {<Sunny, Warm, ?, Strong, ?, ? >}G4 = {<Sunny, ?, ?, ?, ?, ?>, <?, Warm, ?, ?, ?, ?>}
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Candidate-Elimination AlgorithmS4 = {<Sunny, Warm, ?, Strong, ?, ?>}
<Sunny, ?, ?, Strong, ?, ?> <Sunny, Warm, ?, ?, ?, ?> <?, Warm, ?, Strong, ?, ?>
G4 = {<Sunny, ?, ?, ?, ?, ?>, <?, Warm, ?, ?, ?, ?>}
5 Sunny
Cold Normal Strong
Warm Same ?
6 Rainy Warm High Strong
Warm Change ?
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Candidate-Elimination Algorithm
• The version space will converge toward the correct target concepts if:– H contains the correct target concept– There are no errors in the training examples
• A training instance to be requested next should discriminate among the alternative hypotheses in the current version space:
• Partially learned concept can be used to classify new instances using the majority rule.
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Inductive Bias
• Size of the instance space: |X| = 3.2.2.2.2.2 = 96
• Number of possible concepts = 2|X| = 296
• Size of H = (4.3.3.3.3.3) + 1 = 973 << 296
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Inductive Bias
• Size of the instance space: |X| = 3.2.2.2.2.2 = 96
• Number of possible concepts = 2|X| = 296
• Size of H = (4.3.3.3.3.3) + 1 = 973 << 296
a biased hypothesis space
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Inductive Bias
• An unbiased hypothesis space H’ that can represent every subset of the instance space X: Propositional logic sentences
• Positive examples: x1, x2, x3
Negative examples: x4, x5
h = x1 x2 x3 x6
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Inductive Bias
x1 x2 x3 x6
x1 x2 x3
x4 x5
Any new instance x is classified positive by half of the version space, and negative by the other half.
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Inductive BiasExampl
eDay Actor Price EasyTicket
1 Mon Famous Expensive
Yes
2 Sat Famous Moderate
No
3 Sun Infamous Cheap No
4 Wed Infamous Moderate
Yes
5 Sun Famous Expensive
No
6 Thu Infamous Cheap Yes
7 Tue Famous Expensive
Yes
8 Sat Famous Cheap No
9 Wed Famous Cheap ?
10 Sat Infamous Expensive
?
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Inductive Bias
Example
Quality Price Buy
1 Good Low Yes
2 Bad High No
3 Good High ?
4 Bad Low ?
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Inductive Bias
• A learner that makes no prior assumptions regarding the identity of the target concept cannot classify any unseen instances.
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Homework
Exercises 2-1 2.5 (Chapter 2, ML textbook)
3-1 3.4 (Chapter 3, ML textbook)